Related papers: A (5,5) and (6,6) PPT edge state
We construct $3\otimes 3$ PPT entangled edge states with maximal ranks, to complete the classification of $3\otimes 3$ PPT entangled edge states by their types. The ranks of the states and their partial transposes are 8 and 6, respectively.…
We present the PPT square conjecture introduced by M. Christandl. We prove the conjecture in the case $n=3$ as a consequence of the fact that two-qutrit PPT states have Schmidt at most two. Our result in Lemma 3 is independent from the…
Entangled states with a positive partial transpose (so-called PPT states) are central to many interesting problems in quantum theory. On one hand, they are considered to be weakly entangled, since no pure state entanglement can be distilled…
We study extremality in various sets of states that have positive partial transposes. One of the tools we use for this purpose is the recently formulated criterion allowing to judge if a given state is extremal in the set of PPT states.…
In $3\times 3$ dimensions, entangled mixed states that are positive under partial transposition (PPT states) must have rank at least four. They are well understood. We say that they have rank $(4,4)$ since a state $\rho$ and its partial…
We solve the open question of the existence of four-qubit entangled symmetric states with positive partial transpositions (PPT states). We reach this goal with two different approaches. First, we propose a half-analytical-half-numerical…
Genuine high-dimensional entanglement, i.e. the property of having a high Schmidt number, constitutes a resource in quantum communication, overcoming limitations of low-dimensional systems. States with a positive partial transpose (PPT), on…
We have studied mixed states in the system of three qubits with the property that all their partial transposes are positive, these are called PPT states. We classify a PPT state by the ranks of the state itself and its three single partial…
For many completely positive maps repeated compositions will eventually become entanglement breaking. To quantify this behaviour we develop a technique based on the Schmidt number: If a completely positive map breaks the entanglement with…
We construct entangled states with positive partial transposes using indecomposable positive linear maps between matrix algebras. We also exhibit concrete examples of entangled states with positive partial transposes arising in this way,…
The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous…
We report here on the results of numerical searches for PPT states with specified ranks for density matrices and their partial transpose. The study includes several bipartite quantum systems of low dimensions. For a series of ranks extremal…
From both theoretical and experimental points of view symmetric states constitute an important class of multipartite states. Still, entanglement properties of these states, in particular those with positive partial transposition (PPT), lack…
It is known that entangled mixed states that are positive under partial transposition (PPT states) must have rank at least four. In a previous paper we presented a classification of rank four entangled PPT states which we believe to be…
Recently [quant-ph/0608250] again created a lot of interest to prove the existence of bound entangled states with negative partial transpose (NPT) in any $d \times d (d \geq 3)$ Hilbert space. However the proof in quant-ph/0608250 is not…
It is found that the problem of existence of bound entangled states with non-positive partial transpose (NPPT) has the intriguing relation to the Hilbert's 17th problem. More precisely, we compute the expectation value of the partially…
We construct a class of $3\otimes 3$ entangled edge states with positive partial transposes using indecomposable positive linear maps. This class contains several new types of entangled edge states with respect to the range dimensions of…
In the convex set of all $3\ot 3$ states with positive partial transposes, we show that one can take two extreme points whose convex combinations belong to the interior of the convex set. Their convex combinations may be even in the…
We construct faces of the convex set of all $2\otimes 4$ bipartite separable states, which are affinely isomorphic to the simplex $\Delta_{9}$ with ten extreme points. Every interior point of these faces is a separable state which has a…
Let E' denote the set of non-normalized two-qutrit entangled states of rank four having positive partial transpose (PPT). We show that the set of SLOCC equivalence classes of states in E', equipped with the quotient topology, is…